No way to configure which files are displayed
There's no way to configure the parameters sent to the tree command internally, so there's no way to hide files or folders -- the only option is the equivalent of ls -aR, which tends to contain way more entries than you'd normally want.
If possible the tree command should be fed with the contents of a lying around .gitignore in the current or in any parent folder. I already wrote a little hack which I aliased to tree, but that was buggy and hadn't much time to refine it.
Other .*ignore files should be considered. It's quite easy to fill the -I option of tree, as long as the shell expansion rules are taken into account.
[edit] Would also be nice to be able to enable/disable the hidden files with a keystroke.